Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(49,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.i (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 274.4 | ||
Root | \(-2.35083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.274 |
Dual form | 375.2.i.c.349.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.23577 | + | 0.726446i | 1.58093 | + | 0.513675i | 0.962296 | − | 0.272005i | \(-0.0876866\pi\) |
0.618634 | + | 0.785680i | \(0.287687\pi\) | |||||||
\(3\) | 0.587785 | − | 0.809017i | 0.339358 | − | 0.467086i | ||||
\(4\) | 2.85292 | + | 2.07277i | 1.42646 | + | 1.03638i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.90186 | − | 1.38178i | 0.776432 | − | 0.564111i | ||||
\(7\) | 3.48189i | 1.31603i | 0.753005 | + | 0.658015i | \(0.228604\pi\) | ||||
−0.753005 | + | 0.658015i | \(0.771396\pi\) | |||||||
\(8\) | 2.10915 | + | 2.90300i | 0.745698 | + | 1.02637i | ||||
\(9\) | −0.309017 | − | 0.951057i | −0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.905762 | − | 2.78765i | 0.273097 | − | 0.840508i | −0.716619 | − | 0.697465i | \(-0.754311\pi\) |
0.989717 | − | 0.143043i | \(-0.0456887\pi\) | |||||||
\(12\) | 3.35381 | − | 1.08972i | 0.968160 | − | 0.314574i | ||||
\(13\) | −1.78394 | + | 0.579638i | −0.494776 | + | 0.160763i | −0.545768 | − | 0.837937i | \(-0.683762\pi\) |
0.0509914 | + | 0.998699i | \(0.483762\pi\) | |||||||
\(14\) | −2.52940 | + | 7.78470i | −0.676012 | + | 2.08055i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.427277 | + | 1.31502i | 0.106819 | + | 0.328756i | ||||
\(17\) | −3.98851 | − | 5.48972i | −0.967356 | − | 1.33145i | −0.943371 | − | 0.331739i | \(-0.892365\pi\) |
−0.0239850 | − | 0.999712i | \(-0.507635\pi\) | |||||||
\(18\) | − | 2.35083i | − | 0.554096i | ||||||
\(19\) | −2.38620 | + | 1.73367i | −0.547431 | + | 0.397732i | −0.826837 | − | 0.562441i | \(-0.809862\pi\) |
0.279406 | + | 0.960173i | \(0.409862\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.81691 | + | 2.04660i | 0.614699 | + | 0.446605i | ||||
\(22\) | 4.05015 | − | 5.57456i | 0.863496 | − | 1.18850i | ||||
\(23\) | 5.22149 | + | 1.69656i | 1.08876 | + | 0.353758i | 0.797765 | − | 0.602968i | \(-0.206015\pi\) |
0.290990 | + | 0.956726i | \(0.406015\pi\) | |||||||
\(24\) | 3.58831 | 0.732460 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.40956 | −0.864786 | ||||||||
\(27\) | −0.951057 | − | 0.309017i | −0.183031 | − | 0.0594703i | ||||
\(28\) | −7.21714 | + | 9.93354i | −1.36391 | + | 1.87726i | ||||
\(29\) | 2.06779 | + | 1.50234i | 0.383980 | + | 0.278978i | 0.762984 | − | 0.646417i | \(-0.223733\pi\) |
−0.379004 | + | 0.925395i | \(0.623733\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.338237 | + | 0.245744i | −0.0607492 | + | 0.0441369i | −0.617745 | − | 0.786378i | \(-0.711954\pi\) |
0.556996 | + | 0.830515i | \(0.311954\pi\) | |||||||
\(32\) | − | 3.92613i | − | 0.694048i | ||||||
\(33\) | −1.72286 | − | 2.37132i | −0.299912 | − | 0.412793i | ||||
\(34\) | −4.92942 | − | 15.1712i | −0.845388 | − | 2.60184i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.08972 | − | 3.35381i | 0.181620 | − | 0.558968i | ||||
\(37\) | −4.98314 | + | 1.61912i | −0.819224 | + | 0.266182i | −0.688500 | − | 0.725237i | \(-0.741730\pi\) |
−0.130724 | + | 0.991419i | \(0.541730\pi\) | |||||||
\(38\) | −6.59441 | + | 2.14265i | −1.06975 | + | 0.347584i | ||||
\(39\) | −0.579638 | + | 1.78394i | −0.0928163 | + | 0.285659i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.518744 | + | 1.59653i | 0.0810142 | + | 0.249336i | 0.983357 | − | 0.181683i | \(-0.0581543\pi\) |
−0.902343 | + | 0.431019i | \(0.858154\pi\) | |||||||
\(42\) | 4.81121 | + | 6.62206i | 0.742386 | + | 1.02181i | ||||
\(43\) | − | 10.9233i | − | 1.66578i | −0.553436 | − | 0.832892i | \(-0.686684\pi\) | ||
0.553436 | − | 0.832892i | \(-0.313316\pi\) | |||||||
\(44\) | 8.36221 | − | 6.07550i | 1.26065 | − | 0.915916i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.4416 | + | 7.58626i | 1.53953 | + | 1.11853i | ||||
\(47\) | −4.40356 | + | 6.06098i | −0.642325 | + | 0.884084i | −0.998737 | − | 0.0502446i | \(-0.984000\pi\) |
0.356412 | + | 0.934329i | \(0.384000\pi\) | |||||||
\(48\) | 1.31502 | + | 0.427277i | 0.189807 | + | 0.0616721i | ||||
\(49\) | −5.12353 | −0.731933 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.78566 | −0.950183 | ||||||||
\(52\) | −6.29089 | − | 2.04403i | −0.872390 | − | 0.283457i | ||||
\(53\) | −2.18041 | + | 3.00107i | −0.299502 | + | 0.412229i | −0.932071 | − | 0.362275i | \(-0.882000\pi\) |
0.632570 | + | 0.774504i | \(0.282000\pi\) | |||||||
\(54\) | −1.90186 | − | 1.38178i | −0.258811 | − | 0.188037i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −10.1079 | + | 7.34383i | −1.35073 | + | 0.981361i | ||||
\(57\) | 2.94950i | 0.390671i | ||||||||
\(58\) | 3.53175 | + | 4.86103i | 0.463741 | + | 0.638285i | ||||
\(59\) | 2.19666 | + | 6.76062i | 0.285981 | + | 0.880158i | 0.986103 | + | 0.166135i | \(0.0531288\pi\) |
−0.700122 | + | 0.714023i | \(0.746871\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.98917 | + | 6.12204i | −0.254687 | + | 0.783847i | 0.739204 | + | 0.673482i | \(0.235202\pi\) |
−0.993891 | + | 0.110365i | \(0.964798\pi\) | |||||||
\(62\) | −0.934741 | + | 0.303716i | −0.118712 | + | 0.0385719i | ||||
\(63\) | 3.31147 | − | 1.07596i | 0.417206 | − | 0.135558i | ||||
\(64\) | 3.70667 | − | 11.4080i | 0.463334 | − | 1.42600i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.12929 | − | 6.55329i | −0.262098 | − | 0.806654i | ||||
\(67\) | −5.90225 | − | 8.12376i | −0.721075 | − | 0.992475i | −0.999487 | − | 0.0320131i | \(-0.989808\pi\) |
0.278412 | − | 0.960462i | \(-0.410192\pi\) | |||||||
\(68\) | − | 23.9290i | − | 2.90181i | ||||||
\(69\) | 4.44166 | − | 3.22706i | 0.534713 | − | 0.388492i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.589451 | − | 0.428261i | −0.0699550 | − | 0.0508253i | 0.552258 | − | 0.833673i | \(-0.313766\pi\) |
−0.622213 | + | 0.782848i | \(0.713766\pi\) | |||||||
\(72\) | 2.10915 | − | 2.90300i | 0.248566 | − | 0.342122i | ||||
\(73\) | 3.41685 | + | 1.11020i | 0.399912 | + | 0.129939i | 0.502066 | − | 0.864829i | \(-0.332573\pi\) |
−0.102154 | + | 0.994769i | \(0.532573\pi\) | |||||||
\(74\) | −12.3174 | −1.43187 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.4011 | −1.19309 | ||||||||
\(77\) | 9.70628 | + | 3.15376i | 1.10613 | + | 0.359404i | ||||
\(78\) | −2.59188 | + | 3.56741i | −0.293472 | + | 0.403930i | ||||
\(79\) | 2.48583 | + | 1.80606i | 0.279677 | + | 0.203197i | 0.718777 | − | 0.695241i | \(-0.244702\pi\) |
−0.439099 | + | 0.898439i | \(0.644702\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 3.94632i | 0.435798i | ||||||||
\(83\) | 5.94559 | + | 8.18340i | 0.652613 | + | 0.898245i | 0.999209 | − | 0.0397694i | \(-0.0126623\pi\) |
−0.346595 | + | 0.938015i | \(0.612662\pi\) | |||||||
\(84\) | 3.79427 | + | 11.6776i | 0.413989 | + | 1.27413i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.93517 | − | 24.4219i | 0.855672 | − | 2.63349i | ||||
\(87\) | 2.43084 | − | 0.789827i | 0.260613 | − | 0.0846784i | ||||
\(88\) | 10.0029 | − | 3.25015i | 1.06632 | − | 0.346467i | ||||
\(89\) | −0.0888461 | + | 0.273440i | −0.00941767 | + | 0.0289846i | −0.955655 | − | 0.294489i | \(-0.904851\pi\) |
0.946237 | + | 0.323473i | \(0.104851\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.01823 | − | 6.21148i | −0.211568 | − | 0.651140i | ||||
\(92\) | 11.3799 | + | 15.6631i | 1.18644 | + | 1.63299i | ||||
\(93\) | 0.418084i | 0.0433533i | ||||||||
\(94\) | −14.2483 | + | 10.3520i | −1.46960 | + | 1.06773i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.17630 | − | 2.30772i | −0.324180 | − | 0.235531i | ||||
\(97\) | −6.11828 | + | 8.42109i | −0.621217 | + | 0.855032i | −0.997441 | − | 0.0714966i | \(-0.977222\pi\) |
0.376224 | + | 0.926529i | \(0.377222\pi\) | |||||||
\(98\) | −11.4551 | − | 3.72197i | −1.15714 | − | 0.375976i | ||||
\(99\) | −2.93111 | −0.294587 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.65744 | 0.761943 | 0.380972 | − | 0.924587i | \(-0.375590\pi\) | ||||
0.380972 | + | 0.924587i | \(0.375590\pi\) | |||||||
\(102\) | −15.1712 | − | 4.92942i | −1.50217 | − | 0.488085i | ||||
\(103\) | 1.75514 | − | 2.41574i | 0.172939 | − | 0.238030i | −0.713745 | − | 0.700405i | \(-0.753003\pi\) |
0.886684 | + | 0.462375i | \(0.153003\pi\) | |||||||
\(104\) | −5.44530 | − | 3.95624i | −0.533955 | − | 0.387941i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.05501 | + | 5.12576i | −0.685243 | + | 0.497858i | ||||
\(107\) | − | 7.07213i | − | 0.683689i | −0.939757 | − | 0.341844i | \(-0.888948\pi\) | ||
0.939757 | − | 0.341844i | \(-0.111052\pi\) | |||||||
\(108\) | −2.07277 | − | 2.85292i | −0.199452 | − | 0.274522i | ||||
\(109\) | 4.11060 | + | 12.6511i | 0.393724 | + | 1.21176i | 0.929951 | + | 0.367683i | \(0.119849\pi\) |
−0.536227 | + | 0.844074i | \(0.680151\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.61912 | + | 4.98314i | −0.153680 | + | 0.472979i | ||||
\(112\) | −4.57876 | + | 1.48773i | −0.432653 | + | 0.140577i | ||||
\(113\) | 9.53271 | − | 3.09737i | 0.896762 | − | 0.291376i | 0.175862 | − | 0.984415i | \(-0.443729\pi\) |
0.720900 | + | 0.693039i | \(0.243729\pi\) | |||||||
\(114\) | −2.14265 | + | 6.59441i | −0.200678 | + | 0.617623i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.78525 | + | 8.57211i | 0.258604 | + | 0.795900i | ||||
\(117\) | 1.10254 | + | 1.51751i | 0.101930 | + | 0.140294i | ||||
\(118\) | 16.7110i | 1.53837i | ||||||||
\(119\) | 19.1146 | − | 13.8875i | 1.75223 | − | 1.27307i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.94861 | + | 1.41575i | 0.177146 | + | 0.128704i | ||||
\(122\) | −8.89467 | + | 12.2425i | −0.805286 | + | 1.10838i | ||||
\(123\) | 1.59653 | + | 0.518744i | 0.143954 | + | 0.0467736i | ||||
\(124\) | −1.47433 | −0.132399 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 8.18532 | 0.729206 | ||||||||
\(127\) | 10.0556 | + | 3.26725i | 0.892286 | + | 0.289921i | 0.719049 | − | 0.694959i | \(-0.244577\pi\) |
0.173237 | + | 0.984880i | \(0.444577\pi\) | |||||||
\(128\) | 11.9591 | − | 16.4603i | 1.05705 | − | 1.45490i | ||||
\(129\) | −8.83711 | − | 6.42054i | −0.778064 | − | 0.565297i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.30225 | − | 5.30540i | 0.638001 | − | 0.463535i | −0.221162 | − | 0.975237i | \(-0.570985\pi\) |
0.859163 | + | 0.511703i | \(0.170985\pi\) | |||||||
\(132\) | − | 10.3363i | − | 0.899656i | ||||||
\(133\) | −6.03645 | − | 8.30847i | −0.523427 | − | 0.720435i | ||||
\(134\) | −7.29462 | − | 22.4505i | −0.630159 | − | 1.93943i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.52427 | − | 23.1573i | 0.645200 | − | 1.98572i | ||||
\(137\) | 18.7021 | − | 6.07669i | 1.59783 | − | 0.519167i | 0.631261 | − | 0.775571i | \(-0.282538\pi\) |
0.966570 | + | 0.256404i | \(0.0825377\pi\) | |||||||
\(138\) | 12.2748 | − | 3.98833i | 1.04490 | − | 0.339509i | ||||
\(139\) | 3.60067 | − | 11.0817i | 0.305404 | − | 0.939938i | −0.674122 | − | 0.738620i | \(-0.735478\pi\) |
0.979526 | − | 0.201318i | \(-0.0645224\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.31509 | + | 7.12511i | 0.194965 | + | 0.600042i | ||||
\(142\) | −1.00677 | − | 1.38570i | −0.0844862 | − | 0.116285i | ||||
\(143\) | 5.49801i | 0.459767i | ||||||||
\(144\) | 1.11863 | − | 0.812729i | 0.0932188 | − | 0.0677275i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.83280 | + | 4.96432i | 0.565486 | + | 0.410850i | ||||
\(147\) | −3.01154 | + | 4.14503i | −0.248387 | + | 0.341876i | ||||
\(148\) | −17.5726 | − | 5.70967i | −1.44446 | − | 0.469332i | ||||
\(149\) | 7.33020 | 0.600513 | 0.300257 | − | 0.953858i | \(-0.402928\pi\) | ||||
0.300257 | + | 0.953858i | \(0.402928\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.7358 | −1.36194 | −0.680968 | − | 0.732313i | \(-0.738441\pi\) | ||||
−0.680968 | + | 0.732313i | \(0.738441\pi\) | |||||||
\(152\) | −10.0657 | − | 3.27055i | −0.816437 | − | 0.265276i | ||||
\(153\) | −3.98851 | + | 5.48972i | −0.322452 | + | 0.443817i | ||||
\(154\) | 19.4100 | + | 14.1022i | 1.56410 | + | 1.13639i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.35135 | + | 3.88798i | −0.428451 | + | 0.311288i | ||||
\(157\) | 7.88635i | 0.629399i | 0.949191 | + | 0.314700i | \(0.101904\pi\) | ||||
−0.949191 | + | 0.314700i | \(0.898096\pi\) | |||||||
\(158\) | 4.24574 | + | 5.84375i | 0.337773 | + | 0.464904i | ||||
\(159\) | 1.14631 | + | 3.52797i | 0.0909081 | + | 0.279786i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.90724 | + | 18.1806i | −0.465556 | + | 1.43283i | ||||
\(162\) | −2.23577 | + | 0.726446i | −0.175659 | + | 0.0570750i | ||||
\(163\) | −9.45343 | + | 3.07160i | −0.740450 | + | 0.240587i | −0.654867 | − | 0.755744i | \(-0.727275\pi\) |
−0.0855829 | + | 0.996331i | \(0.527275\pi\) | |||||||
\(164\) | −1.82930 | + | 5.63000i | −0.142844 | + | 0.439629i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.34818 | + | 22.6154i | 0.570330 | + | 1.75529i | ||||
\(167\) | −3.27847 | − | 4.51243i | −0.253696 | − | 0.349182i | 0.663106 | − | 0.748526i | \(-0.269238\pi\) |
−0.916801 | + | 0.399344i | \(0.869238\pi\) | |||||||
\(168\) | 12.4941i | 0.963939i | ||||||||
\(169\) | −7.67075 | + | 5.57313i | −0.590058 | + | 0.428702i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.38620 | + | 1.73367i | 0.182477 | + | 0.132577i | ||||
\(172\) | 22.6414 | − | 31.1632i | 1.72639 | − | 2.37617i | ||||
\(173\) | −15.7573 | − | 5.11985i | −1.19800 | − | 0.389255i | −0.358978 | − | 0.933346i | \(-0.616875\pi\) |
−0.839026 | + | 0.544091i | \(0.816875\pi\) | |||||||
\(174\) | 6.00857 | 0.455508 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.05284 | 0.305494 | ||||||||
\(177\) | 6.76062 | + | 2.19666i | 0.508160 | + | 0.165111i | ||||
\(178\) | −0.397279 | + | 0.546808i | −0.0297773 | + | 0.0409850i | ||||
\(179\) | −4.33650 | − | 3.15065i | −0.324125 | − | 0.235491i | 0.413808 | − | 0.910364i | \(-0.364198\pi\) |
−0.737934 | + | 0.674873i | \(0.764198\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.265151 | − | 0.192643i | 0.0197085 | − | 0.0143191i | −0.577887 | − | 0.816117i | \(-0.696123\pi\) |
0.597596 | + | 0.801797i | \(0.296123\pi\) | |||||||
\(182\) | − | 15.3536i | − | 1.13808i | ||||||
\(183\) | 3.78363 | + | 5.20772i | 0.279694 | + | 0.384966i | ||||
\(184\) | 6.08779 | + | 18.7363i | 0.448798 | + | 1.38126i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.303716 | + | 0.934741i | −0.0222695 | + | 0.0685385i | ||||
\(187\) | −18.9160 | + | 6.14619i | −1.38328 | + | 0.449454i | ||||
\(188\) | −25.1260 | + | 8.16392i | −1.83250 | + | 0.595415i | ||||
\(189\) | 1.07596 | − | 3.31147i | 0.0782647 | − | 0.240874i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.07226 | − | 3.30009i | −0.0775862 | − | 0.238786i | 0.904740 | − | 0.425965i | \(-0.140065\pi\) |
−0.982326 | + | 0.187179i | \(0.940065\pi\) | |||||||
\(192\) | −7.05051 | − | 9.70420i | −0.508827 | − | 0.700340i | ||||
\(193\) | 24.3134i | 1.75012i | 0.484018 | + | 0.875058i | \(0.339177\pi\) | ||||
−0.484018 | + | 0.875058i | \(0.660823\pi\) | |||||||
\(194\) | −19.7966 | + | 14.3830i | −1.42131 | + | 1.03264i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.6170 | − | 10.6199i | −1.04407 | − | 0.758563i | ||||
\(197\) | 8.79098 | − | 12.0997i | 0.626331 | − | 0.862071i | −0.371463 | − | 0.928448i | \(-0.621144\pi\) |
0.997795 | + | 0.0663764i | \(0.0211438\pi\) | |||||||
\(198\) | −6.55329 | − | 2.12929i | −0.465722 | − | 0.151322i | ||||
\(199\) | 11.3251 | 0.802817 | 0.401408 | − | 0.915899i | \(-0.368521\pi\) | ||||
0.401408 | + | 0.915899i | \(0.368521\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.0415 | −0.708274 | ||||||||
\(202\) | 17.1203 | + | 5.56272i | 1.20458 | + | 0.391391i | ||||
\(203\) | −5.23098 | + | 7.19983i | −0.367143 | + | 0.505329i | ||||
\(204\) | −19.3589 | − | 14.0651i | −1.35540 | − | 0.984753i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.67900 | − | 4.12603i | 0.395674 | − | 0.287474i | ||||
\(207\) | − | 5.49019i | − | 0.381595i | ||||||
\(208\) | −1.52447 | − | 2.09826i | −0.105703 | − | 0.145488i | ||||
\(209\) | 2.67155 | + | 8.22217i | 0.184795 | + | 0.568739i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.33086 | − | 7.17366i | 0.160463 | − | 0.493855i | −0.838210 | − | 0.545347i | \(-0.816398\pi\) |
0.998673 | + | 0.0514924i | \(0.0163978\pi\) | |||||||
\(212\) | −12.4410 | + | 4.04234i | −0.854454 | + | 0.277629i | ||||
\(213\) | −0.692941 | + | 0.225150i | −0.0474796 | + | 0.0154270i | ||||
\(214\) | 5.13752 | − | 15.8117i | 0.351194 | − | 1.08086i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.10885 | − | 3.41268i | −0.0754475 | − | 0.232204i | ||||
\(217\) | −0.855651 | − | 1.17770i | −0.0580854 | − | 0.0799477i | ||||
\(218\) | 31.2711i | 2.11795i | ||||||||
\(219\) | 2.90655 | − | 2.11173i | 0.196406 | − | 0.142697i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.2973 | + | 7.48144i | 0.692672 | + | 0.503256i | ||||
\(222\) | −7.23997 | + | 9.96497i | −0.485915 | + | 0.668805i | ||||
\(223\) | 7.41386 | + | 2.40891i | 0.496469 | + | 0.161313i | 0.546540 | − | 0.837433i | \(-0.315945\pi\) |
−0.0500709 | + | 0.998746i | \(0.515945\pi\) | |||||||
\(224\) | 13.6703 | 0.913387 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 23.5630 | 1.56739 | ||||||||
\(227\) | −12.2039 | − | 3.96529i | −0.810001 | − | 0.263185i | −0.125403 | − | 0.992106i | \(-0.540022\pi\) |
−0.684598 | + | 0.728921i | \(0.740022\pi\) | |||||||
\(228\) | −6.11363 | + | 8.41468i | −0.404885 | + | 0.557276i | ||||
\(229\) | −11.7334 | − | 8.52483i | −0.775366 | − | 0.563337i | 0.128218 | − | 0.991746i | \(-0.459074\pi\) |
−0.903585 | + | 0.428409i | \(0.859074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.25665 | − | 5.99881i | 0.543248 | − | 0.394693i | ||||
\(232\) | 9.17148i | 0.602137i | ||||||||
\(233\) | 6.69902 | + | 9.22041i | 0.438867 | + | 0.604049i | 0.969960 | − | 0.243265i | \(-0.0782184\pi\) |
−0.531093 | + | 0.847314i | \(0.678218\pi\) | |||||||
\(234\) | 1.36263 | + | 4.19374i | 0.0890779 | + | 0.274153i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.74630 | + | 23.8407i | −0.504241 | + | 1.55190i | ||||
\(237\) | 2.92226 | − | 0.949501i | 0.189821 | − | 0.0616767i | ||||
\(238\) | 52.8244 | − | 17.1637i | 3.42410 | − | 1.11256i | ||||
\(239\) | −2.13244 | + | 6.56298i | −0.137936 | + | 0.424524i | −0.996035 | − | 0.0889605i | \(-0.971646\pi\) |
0.858099 | + | 0.513484i | \(0.171646\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.79052 | − | 27.0545i | −0.566247 | − | 1.74273i | −0.664216 | − | 0.747541i | \(-0.731234\pi\) |
0.0979683 | − | 0.995190i | \(-0.468766\pi\) | |||||||
\(242\) | 3.32818 | + | 4.58085i | 0.213943 | + | 0.294468i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −18.3645 | + | 13.3426i | −1.17567 | + | 0.854172i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.19264 | + | 2.31959i | 0.203555 | + | 0.147891i | ||||
\(247\) | 3.25193 | − | 4.47590i | 0.206915 | − | 0.284795i | ||||
\(248\) | −1.42679 | − | 0.463592i | −0.0906011 | − | 0.0294381i | ||||
\(249\) | 10.1152 | 0.641028 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.3258 | −0.777999 | −0.389000 | − | 0.921238i | \(-0.627179\pi\) | ||||
−0.389000 | + | 0.921238i | \(0.627179\pi\) | |||||||
\(252\) | 11.6776 | + | 3.79427i | 0.735618 | + | 0.239017i | ||||
\(253\) | 9.45885 | − | 13.0190i | 0.594673 | − | 0.818496i | ||||
\(254\) | 20.1084 | + | 14.6096i | 1.26172 | + | 0.916690i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.2870 | − | 14.0128i | 1.20544 | − | 0.875801i | ||||
\(257\) | 20.8274i | 1.29918i | 0.760285 | + | 0.649590i | \(0.225059\pi\) | ||||
−0.760285 | + | 0.649590i | \(0.774941\pi\) | |||||||
\(258\) | −15.0936 | − | 20.7745i | −0.939686 | − | 1.29337i | ||||
\(259\) | −5.63760 | − | 17.3507i | −0.350303 | − | 1.07812i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.789827 | − | 2.43084i | 0.0488891 | − | 0.150465i | ||||
\(262\) | 20.1802 | − | 6.55696i | 1.24674 | − | 0.405090i | ||||
\(263\) | 2.12577 | − | 0.690704i | 0.131080 | − | 0.0425906i | −0.242742 | − | 0.970091i | \(-0.578047\pi\) |
0.373823 | + | 0.927500i | \(0.378047\pi\) | |||||||
\(264\) | 3.25015 | − | 10.0029i | 0.200033 | − | 0.615638i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.46048 | − | 22.9610i | −0.457431 | − | 1.40783i | ||||
\(267\) | 0.168995 | + | 0.232602i | 0.0103423 | + | 0.0142350i | ||||
\(268\) | − | 35.4104i | − | 2.16303i | ||||||
\(269\) | −15.6170 | + | 11.3464i | −0.952183 | + | 0.691802i | −0.951322 | − | 0.308198i | \(-0.900274\pi\) |
−0.000861106 | 1.00000i | \(0.500274\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.66058 | + | 7.01882i | 0.586838 | + | 0.426363i | 0.841183 | − | 0.540751i | \(-0.181860\pi\) |
−0.254345 | + | 0.967114i | \(0.581860\pi\) | |||||||
\(272\) | 5.51491 | − | 7.59062i | 0.334390 | − | 0.460249i | ||||
\(273\) | −6.21148 | − | 2.01823i | −0.375936 | − | 0.122149i | ||||
\(274\) | 46.2281 | 2.79274 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 19.3606 | 1.16537 | ||||||||
\(277\) | 24.8669 | + | 8.07975i | 1.49411 | + | 0.485465i | 0.938293 | − | 0.345841i | \(-0.112406\pi\) |
0.555815 | + | 0.831306i | \(0.312406\pi\) | |||||||
\(278\) | 16.1005 | − | 22.1605i | 0.965646 | − | 1.32910i | ||||
\(279\) | 0.338237 | + | 0.245744i | 0.0202497 | + | 0.0147123i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.18876 | + | 5.94948i | −0.488500 | + | 0.354916i | −0.804607 | − | 0.593807i | \(-0.797624\pi\) |
0.316107 | + | 0.948724i | \(0.397624\pi\) | |||||||
\(282\) | 17.6119i | 1.04877i | ||||||||
\(283\) | −18.7290 | − | 25.7783i | −1.11333 | − | 1.53236i | −0.816423 | − | 0.577455i | \(-0.804046\pi\) |
−0.296903 | − | 0.954907i | \(-0.595954\pi\) | |||||||
\(284\) | −0.793970 | − | 2.44359i | −0.0471135 | − | 0.145000i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.99401 | + | 12.2923i | −0.236171 | + | 0.726859i | ||||
\(287\) | −5.55893 | + | 1.80621i | −0.328134 | + | 0.106617i | ||||
\(288\) | −3.73397 | + | 1.21324i | −0.220026 | + | 0.0714908i | ||||
\(289\) | −8.97546 | + | 27.6236i | −0.527968 | + | 1.62492i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.21657 | + | 9.89959i | 0.188559 | + | 0.580324i | ||||
\(292\) | 7.44680 | + | 10.2496i | 0.435791 | + | 0.599815i | ||||
\(293\) | − | 16.6235i | − | 0.971153i | −0.874194 | − | 0.485576i | \(-0.838610\pi\) | ||
0.874194 | − | 0.485576i | \(-0.161390\pi\) | |||||||
\(294\) | −9.74425 | + | 7.07961i | −0.568296 | + | 0.412891i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −15.2105 | − | 11.0511i | −0.884094 | − | 0.642332i | ||||
\(297\) | −1.72286 | + | 2.37132i | −0.0999706 | + | 0.137598i | ||||
\(298\) | 16.3886 | + | 5.32499i | 0.949369 | + | 0.308469i | ||||
\(299\) | −10.2982 | −0.595561 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.0336 | 2.19222 | ||||||||
\(302\) | −37.4173 | − | 12.1576i | −2.15312 | − | 0.699593i | ||||
\(303\) | 4.50093 | − | 6.19500i | 0.258572 | − | 0.355893i | ||||
\(304\) | −3.29939 | − | 2.39715i | −0.189233 | − | 0.137486i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −12.9054 | + | 9.37631i | −0.737752 | + | 0.536008i | ||||
\(307\) | − | 14.1643i | − | 0.808402i | −0.914670 | − | 0.404201i | \(-0.867550\pi\) | ||
0.914670 | − | 0.404201i | \(-0.132450\pi\) | |||||||
\(308\) | 21.1542 | + | 29.1163i | 1.20537 | + | 1.65905i | ||||
\(309\) | −0.922731 | − | 2.83987i | −0.0524923 | − | 0.161555i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.65070 | − | 14.3134i | 0.263717 | − | 0.811637i | −0.728269 | − | 0.685291i | \(-0.759675\pi\) |
0.991986 | − | 0.126346i | \(-0.0403250\pi\) | |||||||
\(312\) | −6.40133 | + | 2.07992i | −0.362404 | + | 0.117752i | ||||
\(313\) | −3.39980 | + | 1.10466i | −0.192168 | + | 0.0624392i | −0.403520 | − | 0.914971i | \(-0.632213\pi\) |
0.211352 | + | 0.977410i | \(0.432213\pi\) | |||||||
\(314\) | −5.72901 | + | 17.6321i | −0.323307 | + | 0.995036i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.34832 | + | 10.3051i | 0.188358 | + | 0.579706i | ||||
\(317\) | −7.51306 | − | 10.3408i | −0.421975 | − | 0.580799i | 0.544113 | − | 0.839012i | \(-0.316866\pi\) |
−0.966088 | + | 0.258213i | \(0.916866\pi\) | |||||||
\(318\) | 8.72047i | 0.489020i | ||||||||
\(319\) | 6.06093 | − | 4.40352i | 0.339347 | − | 0.246550i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.72147 | − | 4.15689i | −0.319342 | − | 0.232015i | ||||
\(322\) | −26.4145 | + | 36.3564i | −1.47202 | + | 2.02606i | ||||
\(323\) | 19.0347 | + | 6.18476i | 1.05912 | + | 0.344129i | ||||
\(324\) | −3.52640 | −0.195911 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.3671 | −1.29418 | ||||||||
\(327\) | 12.6511 | + | 4.11060i | 0.699608 | + | 0.227317i | ||||
\(328\) | −3.54062 | + | 4.87324i | −0.195498 | + | 0.269080i | ||||
\(329\) | −21.1036 | − | 15.3327i | −1.16348 | − | 0.845318i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.80646 | + | 2.76555i | −0.209222 | + | 0.152009i | −0.687462 | − | 0.726221i | \(-0.741275\pi\) |
0.478240 | + | 0.878229i | \(0.341275\pi\) | |||||||
\(332\) | 35.6704i | 1.95767i | ||||||||
\(333\) | 3.07975 | + | 4.23892i | 0.168769 | + | 0.232291i | ||||
\(334\) | −4.05187 | − | 12.4704i | −0.221709 | − | 0.682349i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.48773 | + | 4.57876i | −0.0811624 | + | 0.249792i | ||||
\(337\) | 16.5529 | − | 5.37837i | 0.901694 | − | 0.292978i | 0.178758 | − | 0.983893i | \(-0.442792\pi\) |
0.722936 | + | 0.690915i | \(0.242792\pi\) | |||||||
\(338\) | −21.1986 | + | 6.88785i | −1.15305 | + | 0.374650i | ||||
\(339\) | 3.09737 | − | 9.53271i | 0.168226 | − | 0.517746i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.378685 | + | 1.16547i | 0.0205069 | + | 0.0631138i | ||||
\(342\) | 4.07557 | + | 5.60954i | 0.220382 | + | 0.303329i | ||||
\(343\) | 6.53364i | 0.352783i | ||||||||
\(344\) | 31.7103 | − | 23.0389i | 1.70970 | − | 1.24217i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −31.5104 | − | 22.8936i | −1.69401 | − | 1.23077i | ||||
\(347\) | 8.23525 | − | 11.3348i | 0.442091 | − | 0.608486i | −0.528584 | − | 0.848881i | \(-0.677277\pi\) |
0.970675 | + | 0.240395i | \(0.0772769\pi\) | |||||||
\(348\) | 8.57211 | + | 2.78525i | 0.459513 | + | 0.149305i | ||||
\(349\) | −35.9459 | −1.92414 | −0.962069 | − | 0.272806i | \(-0.912048\pi\) | ||||
−0.962069 | + | 0.272806i | \(0.912048\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.87575 | 0.100120 | ||||||||
\(352\) | −10.9447 | − | 3.55614i | −0.583352 | − | 0.189543i | ||||
\(353\) | −5.17367 | + | 7.12095i | −0.275367 | + | 0.379010i | −0.924192 | − | 0.381927i | \(-0.875260\pi\) |
0.648826 | + | 0.760937i | \(0.275260\pi\) | |||||||
\(354\) | 13.5195 | + | 9.82246i | 0.718551 | + | 0.522058i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.820248 | + | 0.595945i | −0.0434731 | + | 0.0315850i | ||||
\(357\) | − | 23.6269i | − | 1.25047i | ||||||
\(358\) | −7.40665 | − | 10.1944i | −0.391454 | − | 0.538790i | ||||
\(359\) | −1.86326 | − | 5.73451i | −0.0983389 | − | 0.302656i | 0.889771 | − | 0.456408i | \(-0.150864\pi\) |
−0.988109 | + | 0.153752i | \(0.950864\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.18301 | + | 9.79630i | −0.167527 | + | 0.515595i | ||||
\(362\) | 0.732762 | − | 0.238089i | 0.0385131 | − | 0.0125137i | ||||
\(363\) | 2.29073 | − | 0.744302i | 0.120232 | − | 0.0390657i | ||||
\(364\) | 7.11710 | − | 21.9042i | 0.373037 | − | 1.14809i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.67621 | + | 14.3919i | 0.244429 | + | 0.752276i | ||||
\(367\) | −16.9084 | − | 23.2724i | −0.882609 | − | 1.21481i | −0.975691 | − | 0.219149i | \(-0.929672\pi\) |
0.0930825 | − | 0.995658i | \(-0.470328\pi\) | |||||||
\(368\) | 7.59128i | 0.395723i | ||||||||
\(369\) | 1.35809 | − | 0.986709i | 0.0706993 | − | 0.0513660i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.4494 | − | 7.59193i | −0.542505 | − | 0.394153i | ||||
\(372\) | −0.866590 | + | 1.19276i | −0.0449306 | + | 0.0618417i | ||||
\(373\) | −31.9555 | − | 10.3830i | −1.65459 | − | 0.537610i | −0.674866 | − | 0.737940i | \(-0.735799\pi\) |
−0.979729 | + | 0.200330i | \(0.935799\pi\) | |||||||
\(374\) | −46.7568 | −2.41774 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −26.8828 | −1.38637 | ||||||||
\(377\) | −4.55964 | − | 1.48152i | −0.234833 | − | 0.0763020i | ||||
\(378\) | 4.81121 | − | 6.62206i | 0.247462 | − | 0.340602i | ||||
\(379\) | 3.74901 | + | 2.72381i | 0.192574 | + | 0.139913i | 0.679894 | − | 0.733310i | \(-0.262026\pi\) |
−0.487321 | + | 0.873223i | \(0.662026\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.55377 | − | 6.21467i | 0.438223 | − | 0.318387i | ||||
\(382\) | − | 8.15718i | − | 0.417358i | ||||||
\(383\) | −7.58581 | − | 10.4410i | −0.387617 | − | 0.533509i | 0.569965 | − | 0.821669i | \(-0.306957\pi\) |
−0.957582 | + | 0.288160i | \(0.906957\pi\) | |||||||
\(384\) | −6.28728 | − | 19.3503i | −0.320846 | − | 0.987464i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.6624 | + | 54.3592i | −0.898991 | + | 2.76681i | ||||
\(387\) | −10.3886 | + | 3.37548i | −0.528085 | + | 0.171585i | ||||
\(388\) | −34.9099 | + | 11.3429i | −1.77228 | + | 0.575849i | ||||
\(389\) | 5.41540 | − | 16.6669i | 0.274571 | − | 0.845044i | −0.714761 | − | 0.699369i | \(-0.753465\pi\) |
0.989332 | − | 0.145675i | \(-0.0465355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.5123 | − | 35.4312i | −0.582202 | − | 1.79183i | ||||
\(392\) | −10.8063 | − | 14.8736i | −0.545802 | − | 0.751232i | ||||
\(393\) | − | 9.02608i | − | 0.455305i | ||||||
\(394\) | 28.4444 | − | 20.6661i | 1.43301 | − | 1.04114i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.36221 | − | 6.07550i | −0.420217 | − | 0.305305i | ||||
\(397\) | −15.8805 | + | 21.8577i | −0.797021 | + | 1.09701i | 0.196177 | + | 0.980569i | \(0.437147\pi\) |
−0.993198 | + | 0.116437i | \(0.962853\pi\) | |||||||
\(398\) | 25.3204 | + | 8.22709i | 1.26920 | + | 0.412387i | ||||
\(399\) | −10.2698 | −0.514134 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.9792 | −0.797965 | −0.398983 | − | 0.916958i | \(-0.630637\pi\) | ||||
−0.398983 | + | 0.916958i | \(0.630637\pi\) | |||||||
\(402\) | −22.4505 | − | 7.29462i | −1.11973 | − | 0.363823i | ||||
\(403\) | 0.460953 | − | 0.634447i | 0.0229617 | − | 0.0316041i | ||||
\(404\) | 21.8460 | + | 15.8721i | 1.08688 | + | 0.789665i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.9256 | + | 12.2971i | −0.840002 | + | 0.610297i | ||||
\(407\) | 15.3578i | 0.761258i | ||||||||
\(408\) | −14.3120 | − | 19.6988i | −0.708550 | − | 0.975235i | ||||
\(409\) | 9.57834 | + | 29.4791i | 0.473618 | + | 1.45765i | 0.847812 | + | 0.530297i | \(0.177920\pi\) |
−0.374193 | + | 0.927351i | \(0.622080\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.07669 | − | 18.7021i | 0.299741 | − | 0.922508i | ||||
\(412\) | 10.0145 | − | 3.25392i | 0.493381 | − | 0.160309i | ||||
\(413\) | −23.5397 | + | 7.64852i | −1.15831 | + | 0.376359i | ||||
\(414\) | 3.98833 | − | 12.2748i | 0.196016 | − | 0.603275i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.27573 | + | 7.00398i | 0.111577 | + | 0.343398i | ||||
\(417\) | −6.84887 | − | 9.42666i | −0.335391 | − | 0.461626i | ||||
\(418\) | 20.3236i | 0.994061i | ||||||||
\(419\) | 20.9660 | − | 15.2327i | 1.02425 | − | 0.744164i | 0.0571034 | − | 0.998368i | \(-0.481814\pi\) |
0.967151 | + | 0.254204i | \(0.0818135\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.17658 | − | 2.30792i | −0.154817 | − | 0.112481i | 0.507680 | − | 0.861546i | \(-0.330503\pi\) |
−0.662497 | + | 0.749065i | \(0.730503\pi\) | |||||||
\(422\) | 10.4226 | − | 14.3454i | 0.507362 | − | 0.698324i | ||||
\(423\) | 7.12511 | + | 2.31509i | 0.346434 | + | 0.112563i | ||||
\(424\) | −13.3109 | −0.646436 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.71282 | −0.0829863 | ||||||||
\(427\) | −21.3163 | − | 6.92607i | −1.03157 | − | 0.335176i | ||||
\(428\) | 14.6589 | − | 20.1762i | 0.708563 | − | 0.975254i | ||||
\(429\) | 4.44799 | + | 3.23165i | 0.214751 | + | 0.156026i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.6903 | − | 20.8447i | 1.38196 | − | 1.00406i | 0.385270 | − | 0.922804i | \(-0.374108\pi\) |
0.996694 | − | 0.0812518i | \(-0.0258918\pi\) | |||||||
\(432\) | − | 1.38270i | − | 0.0665251i | ||||||
\(433\) | 5.93423 | + | 8.16776i | 0.285181 | + | 0.392518i | 0.927441 | − | 0.373969i | \(-0.122003\pi\) |
−0.642261 | + | 0.766486i | \(0.722003\pi\) | |||||||
\(434\) | −1.05750 | − | 3.25466i | −0.0507618 | − | 0.156229i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.4956 | + | 44.6129i | −0.694214 | + | 2.13657i | ||||
\(437\) | −15.4008 | + | 5.00402i | −0.736719 | + | 0.239375i | ||||
\(438\) | 8.03243 | − | 2.60990i | 0.383804 | − | 0.124706i | ||||
\(439\) | −2.19575 | + | 6.75783i | −0.104798 | + | 0.322534i | −0.989683 | − | 0.143275i | \(-0.954237\pi\) |
0.884885 | + | 0.465809i | \(0.154237\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.58326 | + | 4.87277i | 0.0753933 | + | 0.232037i | ||||
\(442\) | 17.5876 | + | 24.2072i | 0.836556 | + | 1.15142i | ||||
\(443\) | − | 20.6841i | − | 0.982733i | −0.870953 | − | 0.491366i | \(-0.836498\pi\) | ||
0.870953 | − | 0.491366i | \(-0.163502\pi\) | |||||||
\(444\) | −14.9481 | + | 10.8604i | −0.709406 | + | 0.515414i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.8258 | + | 10.7715i | 0.702020 | + | 0.510047i | ||||
\(447\) | 4.30858 | − | 5.93025i | 0.203789 | − | 0.280491i | ||||
\(448\) | 39.7213 | + | 12.9062i | 1.87665 | + | 0.609762i | ||||
\(449\) | −19.4940 | −0.919980 | −0.459990 | − | 0.887924i | \(-0.652147\pi\) | ||||
−0.459990 | + | 0.887924i | \(0.652147\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.92042 | 0.231694 | ||||||||
\(452\) | 33.6162 | + | 10.9225i | 1.58117 | + | 0.513754i | ||||
\(453\) | −9.83703 | + | 13.5395i | −0.462184 | + | 0.636142i | ||||
\(454\) | −24.4046 | − | 17.7310i | −1.14536 | − | 0.832155i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.56240 | + | 6.22095i | −0.400971 | + | 0.291323i | ||||
\(457\) | − | 4.34194i | − | 0.203107i | −0.994830 | − | 0.101554i | \(-0.967619\pi\) | ||
0.994830 | − | 0.101554i | \(-0.0323813\pi\) | |||||||
\(458\) | −20.0404 | − | 27.5833i | −0.936427 | − | 1.28888i | ||||
\(459\) | 2.09688 | + | 6.45355i | 0.0978742 | + | 0.301226i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.64322 | − | 11.2127i | 0.169682 | − | 0.522227i | −0.829669 | − | 0.558256i | \(-0.811471\pi\) |
0.999351 | + | 0.0360287i | \(0.0114708\pi\) | |||||||
\(462\) | 22.8178 | − | 7.41395i | 1.06158 | − | 0.344928i | ||||
\(463\) | −8.63436 | + | 2.80547i | −0.401273 | + | 0.130381i | −0.502699 | − | 0.864462i | \(-0.667659\pi\) |
0.101426 | + | 0.994843i | \(0.467659\pi\) | |||||||
\(464\) | −1.09209 | + | 3.36112i | −0.0506991 | + | 0.156036i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.27934 | + | 25.4812i | 0.383533 | + | 1.18039i | ||||
\(467\) | 20.5244 | + | 28.2494i | 0.949755 | + | 1.30723i | 0.951636 | + | 0.307227i | \(0.0994010\pi\) |
−0.00188168 | + | 0.999998i | \(0.500599\pi\) | |||||||
\(468\) | 6.61463i | 0.305762i | ||||||||
\(469\) | 28.2860 | − | 20.5510i | 1.30613 | − | 0.948956i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.38019 | + | 4.63548i | 0.293984 | + | 0.213592i | ||||
\(472\) | −14.9930 | + | 20.6361i | −0.690109 | + | 0.949854i | ||||
\(473\) | −30.4502 | − | 9.89388i | −1.40010 | − | 0.454921i | ||||
\(474\) | 7.22328 | 0.331776 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 83.3179 | 3.81887 | ||||||||
\(477\) | 3.52797 | + | 1.14631i | 0.161535 | + | 0.0524858i | ||||
\(478\) | −9.53530 | + | 13.1242i | −0.436135 | + | 0.600288i | ||||
\(479\) | −6.99515 | − | 5.08228i | −0.319617 | − | 0.232215i | 0.416395 | − | 0.909184i | \(-0.363293\pi\) |
−0.736012 | + | 0.676969i | \(0.763293\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.95113 | − | 5.77684i | 0.362540 | − | 0.263401i | ||||
\(482\) | − | 66.8734i | − | 3.04600i | ||||||
\(483\) | 11.2362 | + | 15.4654i | 0.511267 | + | 0.703698i | ||||
\(484\) | 2.62471 | + | 8.07802i | 0.119305 | + | 0.367183i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.726446 | + | 2.23577i | −0.0329523 | + | 0.101417i | ||||
\(487\) | −2.70539 | + | 0.879035i | −0.122593 | + | 0.0398329i | −0.369671 | − | 0.929163i | \(-0.620530\pi\) |
0.247078 | + | 0.968996i | \(0.420530\pi\) | |||||||
\(488\) | −21.9678 | + | 7.13776i | −0.994434 | + | 0.323111i | ||||
\(489\) | −3.07160 | + | 9.45343i | −0.138903 | + | 0.427499i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.3731 | + | 35.0028i | 0.513260 | + | 1.57965i | 0.786425 | + | 0.617686i | \(0.211930\pi\) |
−0.273165 | + | 0.961967i | \(0.588070\pi\) | |||||||
\(492\) | 3.47953 | + | 4.78917i | 0.156869 | + | 0.215912i | ||||
\(493\) | − | 17.3437i | − | 0.781121i | ||||||
\(494\) | 10.5221 | − | 7.64474i | 0.473411 | − | 0.343953i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.467680 | − | 0.339789i | −0.0209994 | − | 0.0152570i | ||||
\(497\) | 1.49116 | − | 2.05240i | 0.0668876 | − | 0.0920628i | ||||
\(498\) | 22.6154 | + | 7.34818i | 1.01342 | + | 0.329280i | ||||
\(499\) | −5.85775 | −0.262229 | −0.131114 | − | 0.991367i | \(-0.541856\pi\) | ||||
−0.131114 | + | 0.991367i | \(0.541856\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.57767 | −0.249192 | ||||||||
\(502\) | −27.5577 | − | 8.95405i | −1.22996 | − | 0.399639i | ||||
\(503\) | 17.8025 | − | 24.5030i | 0.793773 | − | 1.09253i | −0.199855 | − | 0.979825i | \(-0.564047\pi\) |
0.993628 | − | 0.112709i | \(-0.0359528\pi\) | |||||||
\(504\) | 10.1079 | + | 7.34383i | 0.450243 | + | 0.327120i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 30.6054 | − | 22.2361i | 1.36058 | − | 0.988517i | ||||
\(507\) | 9.48157i | 0.421091i | ||||||||
\(508\) | 21.9154 | + | 30.1640i | 0.972340 | + | 1.33831i | ||||
\(509\) | −4.67944 | − | 14.4018i | −0.207413 | − | 0.638350i | −0.999606 | − | 0.0280797i | \(-0.991061\pi\) |
0.792193 | − | 0.610270i | \(-0.208939\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.86560 | + | 11.8971i | −0.171004 | + | 0.526296i | ||||
\(512\) | 14.6004 | − | 4.74395i | 0.645251 | − | 0.209655i | ||||
\(513\) | 2.80514 | − | 0.911446i | 0.123850 | − | 0.0402413i | ||||
\(514\) | −15.1300 | + | 46.5654i | −0.667356 | + | 2.05391i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11.9033 | − | 36.6345i | −0.524013 | − | 1.61275i | ||||
\(517\) | 12.9073 | + | 17.7654i | 0.567662 | + | 0.781320i | ||||
\(518\) | − | 42.8877i | − | 1.88438i | ||||||
\(519\) | −13.4039 | + | 9.73854i | −0.588368 | + | 0.427474i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.6190 | − | 22.9726i | −1.38525 | − | 1.00645i | −0.996367 | − | 0.0851601i | \(-0.972860\pi\) |
−0.388887 | − | 0.921286i | \(-0.627140\pi\) | |||||||
\(522\) | 3.53175 | − | 4.86103i | 0.154580 | − | 0.212762i | ||||
\(523\) | 36.8987 | + | 11.9891i | 1.61347 | + | 0.524248i | 0.970388 | − | 0.241550i | \(-0.0776558\pi\) |
0.643081 | + | 0.765798i | \(0.277656\pi\) | |||||||
\(524\) | 31.8296 | 1.39048 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.25449 | 0.229107 | ||||||||
\(527\) | 2.69813 | + | 0.876674i | 0.117532 | + | 0.0381885i | ||||
\(528\) | 2.38220 | − | 3.27881i | 0.103672 | − | 0.142692i | ||||
\(529\) | 5.77819 | + | 4.19810i | 0.251226 | + | 0.182526i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.75093 | − | 4.17830i | 0.249569 | − | 0.181323i | ||||
\(532\) | − | 36.2155i | − | 1.57014i | ||||||
\(533\) | −1.85082 | − | 2.54743i | −0.0801678 | − | 0.110341i | ||||
\(534\) | 0.208862 | + | 0.642811i | 0.00903835 | + | 0.0278172i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.1345 | − | 34.2685i | 0.480938 | − | 1.48017i | ||||
\(537\) | −5.09787 | + | 1.65640i | −0.219989 | + | 0.0714788i | ||||
\(538\) | −43.1585 | + | 14.0231i | −1.86070 | + | 0.604577i | ||||
\(539\) | −4.64070 | + | 14.2826i | −0.199889 | + | 0.615196i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.39669 | + | 13.5316i | 0.189029 | + | 0.581770i | 0.999994 | − | 0.00332312i | \(-0.00105778\pi\) |
−0.810966 | + | 0.585094i | \(0.801058\pi\) | |||||||
\(542\) | 16.5001 | + | 22.7104i | 0.708738 | + | 0.975494i | ||||
\(543\) | − | 0.327745i | − | 0.0140649i | ||||||
\(544\) | −21.5533 | + | 15.6594i | −0.924091 | + | 0.671391i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −12.4213 | − | 9.02462i | −0.531583 | − | 0.386218i | ||||
\(547\) | 23.1134 | − | 31.8129i | 0.988259 | − | 1.36022i | 0.0559991 | − | 0.998431i | \(-0.482166\pi\) |
0.932259 | − | 0.361790i | \(-0.117834\pi\) | |||||||
\(548\) | 65.9512 | + | 21.4288i | 2.81730 | + | 0.915395i | ||||
\(549\) | 6.43710 | 0.274729 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.53873 | −0.321161 | ||||||||
\(552\) | 18.7363 | + | 6.08779i | 0.797470 | + | 0.259114i | ||||
\(553\) | −6.28849 | + | 8.65537i | −0.267414 | + | 0.368064i | ||||
\(554\) | 49.7272 | + | 36.1290i | 2.11271 | + | 1.53497i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 33.2422 | − | 24.1519i | 1.40978 | − | 1.02427i | ||||
\(557\) | 35.3849i | 1.49931i | 0.661830 | + | 0.749654i | \(0.269780\pi\) | ||||
−0.661830 | + | 0.749654i | \(0.730220\pi\) | |||||||
\(558\) | 0.577701 | + | 0.795138i | 0.0244561 | + | 0.0336609i | ||||
\(559\) | 6.33154 | + | 19.4865i | 0.267796 | + | 0.824190i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.14619 | + | 18.9160i | −0.259492 | + | 0.798636i | ||||
\(562\) | −22.6302 | + | 7.35299i | −0.954597 | + | 0.310167i | ||||
\(563\) | 14.3025 | − | 4.64717i | 0.602780 | − | 0.195855i | 0.00830000 | − | 0.999966i | \(-0.497358\pi\) |
0.594480 | + | 0.804111i | \(0.297358\pi\) | |||||||
\(564\) | −8.16392 | + | 25.1260i | −0.343763 | + | 1.05799i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −23.1473 | − | 71.2401i | −0.972954 | − | 2.99444i | ||||
\(567\) | −2.04660 | − | 2.81691i | −0.0859492 | − | 0.118299i | ||||
\(568\) | − | 2.61445i | − | 0.109700i | ||||||
\(569\) | −2.20383 | + | 1.60118i | −0.0923895 | + | 0.0671249i | −0.633021 | − | 0.774135i | \(-0.718185\pi\) |
0.540632 | + | 0.841260i | \(0.318185\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.2127 | − | 7.41997i | −0.427389 | − | 0.310516i | 0.353215 | − | 0.935542i | \(-0.385088\pi\) |
−0.780604 | + | 0.625026i | \(0.785088\pi\) | |||||||
\(572\) | −11.3961 | + | 15.6854i | −0.476495 | + | 0.655839i | ||||
\(573\) | −3.30009 | − | 1.07226i | −0.137863 | − | 0.0447944i | ||||
\(574\) | −13.7406 | −0.573522 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.9951 | −0.499794 | ||||||||
\(577\) | −22.4301 | − | 7.28797i | −0.933776 | − | 0.303402i | −0.197670 | − | 0.980269i | \(-0.563338\pi\) |
−0.736106 | + | 0.676866i | \(0.763338\pi\) | |||||||
\(578\) | −40.1342 | + | 55.2399i | −1.66936 | + | 2.29768i | ||||
\(579\) | 19.6700 | + | 14.2911i | 0.817455 | + | 0.593916i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.4937 | + | 20.7019i | −1.18212 | + | 0.858858i | ||||
\(582\) | 24.4699i | 1.01431i | ||||||||
\(583\) | 6.39100 | + | 8.79646i | 0.264688 | + | 0.364312i | ||||
\(584\) | 3.98374 | + | 12.2607i | 0.164849 | + | 0.507352i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.0761 | − | 37.1663i | 0.498857 | − | 1.53532i | ||||
\(587\) | 21.5673 | − | 7.00764i | 0.890177 | − | 0.289236i | 0.172000 | − | 0.985097i | \(-0.444977\pi\) |
0.718177 | + | 0.695861i | \(0.244977\pi\) | |||||||
\(588\) | −17.1833 | + | 5.58321i | −0.708629 | + | 0.230248i | ||||
\(589\) | 0.381061 | − | 1.17279i | 0.0157013 | − | 0.0483238i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.62169 | − | 14.2241i | −0.190111 | − | 0.585102i | ||||
\(592\) | −4.25837 | − | 5.86114i | −0.175018 | − | 0.240891i | ||||
\(593\) | 8.74287i | 0.359027i | 0.983756 | + | 0.179513i | \(0.0574523\pi\) | ||||
−0.983756 | + | 0.179513i | \(0.942548\pi\) | |||||||
\(594\) | −5.57456 | + | 4.05015i | −0.228727 | + | 0.166180i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.9124 | + | 15.1938i | 0.856607 | + | 0.622362i | ||||
\(597\) | 6.65674 | − | 9.16222i | 0.272442 | − | 0.374985i | ||||
\(598\) | −23.0245 | − | 7.48110i | −0.941540 | − | 0.305925i | ||||
\(599\) | −16.3209 | −0.666854 | −0.333427 | − | 0.942776i | \(-0.608205\pi\) | ||||
−0.333427 | + | 0.942776i | \(0.608205\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.2713 | 1.47954 | 0.739768 | − | 0.672862i | \(-0.234935\pi\) | ||||
0.739768 | + | 0.672862i | \(0.234935\pi\) | |||||||
\(602\) | 85.0344 | + | 27.6294i | 3.46575 | + | 1.12609i | ||||
\(603\) | −5.90225 | + | 8.12376i | −0.240358 | + | 0.330825i | ||||
\(604\) | −47.7457 | − | 34.6893i | −1.94275 | − | 1.41149i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.5634 | − | 10.5809i | 0.591597 | − | 0.429820i | ||||
\(607\) | − | 16.6820i | − | 0.677102i | −0.940948 | − | 0.338551i | \(-0.890063\pi\) | ||
0.940948 | − | 0.338551i | \(-0.109937\pi\) | |||||||
\(608\) | 6.80662 | + | 9.36851i | 0.276045 | + | 0.379943i | ||||
\(609\) | 2.75009 | + | 8.46390i | 0.111439 | + | 0.342975i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.34252 | − | 13.3649i | 0.175679 | − | 0.540686i | ||||
\(612\) | −22.7578 | + | 7.39445i | −0.919929 | + | 0.298903i | ||||
\(613\) | 23.5831 | − | 7.66260i | 0.952511 | − | 0.309490i | 0.208776 | − | 0.977964i | \(-0.433052\pi\) |
0.743736 | + | 0.668474i | \(0.233052\pi\) | |||||||
\(614\) | 10.2896 | − | 31.6682i | 0.415256 | − | 1.27803i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.3167 | + | 34.8291i | 0.455961 | + | 1.40330i | ||||
\(617\) | −16.4386 | − | 22.6257i | −0.661791 | − | 0.910877i | 0.337748 | − | 0.941237i | \(-0.390335\pi\) |
−0.999539 | + | 0.0303592i | \(0.990335\pi\) | |||||||
\(618\) | − | 7.01963i | − | 0.282371i | ||||||
\(619\) | 22.0608 | − | 16.0281i | 0.886697 | − | 0.644223i | −0.0483179 | − | 0.998832i | \(-0.515386\pi\) |
0.935015 | + | 0.354609i | \(0.115386\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.44166 | − | 3.22706i | −0.178238 | − | 0.129497i | ||||
\(622\) | 20.7958 | − | 28.6230i | 0.833836 | − | 1.14768i | ||||
\(623\) | −0.952088 | − | 0.309352i | −0.0381446 | − | 0.0123939i | ||||
\(624\) | −2.59359 | −0.103827 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.40365 | −0.335878 | ||||||||
\(627\) | 8.22217 | + | 2.67155i | 0.328362 | + | 0.106691i | ||||
\(628\) | −16.3466 | + | 22.4991i | −0.652299 | + | 0.897812i | ||||
\(629\) | 28.7638 | + | 20.8982i | 1.14689 | + | 0.833264i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.1893 | + | 24.8400i | −1.36105 | + | 0.988863i | −0.362676 | + | 0.931915i | \(0.618137\pi\) |
−0.998377 | + | 0.0569481i | \(0.981863\pi\) | |||||||
\(632\) | 11.0256i | 0.438575i | ||||||||
\(633\) | −4.43356 | − | 6.10228i | −0.176218 | − | 0.242544i | ||||
\(634\) | −9.28542 | − | 28.5776i | −0.368771 | − | 1.13496i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.04234 | + | 12.4410i | −0.160289 | + | 0.493319i | ||||
\(637\) | 9.14008 | − | 2.96979i | 0.362143 | − | 0.117667i | ||||
\(638\) | 16.7498 | − | 5.44233i | 0.663130 | − | 0.215464i | ||||
\(639\) | −0.225150 | + | 0.692941i | −0.00890681 | + | 0.0274123i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.1671 | + | 43.6017i | 0.559565 | + | 1.72217i | 0.683571 | + | 0.729884i | \(0.260426\pi\) |
−0.124006 | + | 0.992281i | \(0.539574\pi\) | |||||||
\(642\) | −9.77215 | − | 13.4502i | −0.385676 | − | 0.530837i | ||||
\(643\) | 46.6710i | 1.84052i | 0.391304 | + | 0.920261i | \(0.372024\pi\) | ||||
−0.391304 | + | 0.920261i | \(0.627976\pi\) | |||||||
\(644\) | −54.5370 | + | 39.6235i | −2.14906 | + | 1.56138i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 38.0644 | + | 27.6554i | 1.49763 | + | 1.08809i | ||||
\(647\) | −7.12775 | + | 9.81050i | −0.280221 | + | 0.385691i | −0.925807 | − | 0.377997i | \(-0.876613\pi\) |
0.645586 | + | 0.763687i | \(0.276613\pi\) | |||||||
\(648\) | −3.41268 | − | 1.10885i | −0.134063 | − | 0.0435597i | ||||
\(649\) | 20.8359 | 0.817880 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.45572 | −0.0570542 | ||||||||
\(652\) | −33.3366 | − | 10.8317i | −1.30556 | − | 0.424202i | ||||
\(653\) | 1.01109 | − | 1.39164i | 0.0395670 | − | 0.0544593i | −0.788775 | − | 0.614682i | \(-0.789284\pi\) |
0.828342 | + | 0.560223i | \(0.189284\pi\) | |||||||
\(654\) | 25.2989 | + | 18.3807i | 0.989264 | + | 0.718743i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.87783 | + | 1.36432i | −0.0733168 | + | 0.0532678i | ||||
\(657\) | − | 3.59269i | − | 0.140164i | ||||||
\(658\) | −36.0445 | − | 49.6110i | −1.40516 | − | 1.93404i | ||||
\(659\) | −1.69325 | − | 5.21129i | −0.0659596 | − | 0.203003i | 0.912645 | − | 0.408754i | \(-0.134036\pi\) |
−0.978604 | + | 0.205751i | \(0.934036\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.246425 | − | 0.758418i | 0.00958482 | − | 0.0294990i | −0.946150 | − | 0.323729i | \(-0.895063\pi\) |
0.955735 | + | 0.294230i | \(0.0950633\pi\) | |||||||
\(662\) | −10.5194 | + | 3.41796i | −0.408848 | + | 0.132843i | ||||
\(663\) | 12.1052 | − | 3.93322i | 0.470128 | − | 0.152754i | ||||
\(664\) | −11.2163 | + | 34.5201i | −0.435276 | + | 1.33964i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.80628 | + | 11.7145i | 0.147490 | + | 0.453929i | ||||
\(667\) | 8.24814 | + | 11.3526i | 0.319369 | + | 0.439574i | ||||
\(668\) | − | 19.6691i | − | 0.761020i | ||||||
\(669\) | 6.30661 | − | 4.58202i | 0.243827 | − | 0.177151i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.2644 | + | 11.0902i | 0.589275 | + | 0.428133i | ||||
\(672\) | 8.03522 | − | 11.0595i | 0.309965 | − | 0.426631i | ||||
\(673\) | 48.8158 | + | 15.8612i | 1.88171 | + | 0.611405i | 0.985995 | + | 0.166777i | \(0.0533361\pi\) |
0.895716 | + | 0.444627i | \(0.146664\pi\) | |||||||
\(674\) | 40.9156 | 1.57601 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −33.4358 | −1.28599 | ||||||||
\(677\) | 14.3542 | + | 4.66397i | 0.551678 | + | 0.179251i | 0.571573 | − | 0.820551i | \(-0.306333\pi\) |
−0.0198952 | + | 0.999802i | \(0.506333\pi\) | |||||||
\(678\) | 13.8500 | − | 19.0629i | 0.531906 | − | 0.732106i | ||||
\(679\) | −29.3213 | − | 21.3032i | −1.12525 | − | 0.817540i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.3813 | + | 7.54242i | −0.397811 | + | 0.289026i | ||||
\(682\) | 2.88082i | 0.110312i | ||||||||
\(683\) | −6.38347 | − | 8.78610i | −0.244257 | − | 0.336191i | 0.669233 | − | 0.743053i | \(-0.266623\pi\) |
−0.913490 | + | 0.406862i | \(0.866623\pi\) | |||||||
\(684\) | 3.21412 | + | 9.89205i | 0.122895 | + | 0.378232i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.74634 | + | 14.6077i | −0.181216 | + | 0.557726i | ||||
\(687\) | −13.7935 | + | 4.48177i | −0.526253 | + | 0.170990i | ||||
\(688\) | 14.3644 | − | 4.66726i | 0.547636 | − | 0.177938i | ||||
\(689\) | 2.15018 | − | 6.61758i | 0.0819154 | − | 0.252110i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.60981 | + | 8.03217i | 0.0992818 | + | 0.305558i | 0.988346 | − | 0.152225i | \(-0.0486438\pi\) |
−0.889064 | + | 0.457783i | \(0.848644\pi\) | |||||||
\(692\) | −34.3420 | − | 47.2677i | −1.30549 | − | 1.79685i | ||||
\(693\) | − | 10.2058i | − | 0.387686i | ||||||
\(694\) | 26.6463 | − | 19.3597i | 1.01148 | − | 0.734883i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.41988 | + | 5.39086i | 0.281250 | + | 0.204340i | ||||
\(697\) | 6.69548 | − | 9.21553i | 0.253609 | − | 0.349063i | ||||
\(698\) | −80.3668 | − | 26.1127i | −3.04193 | − | 0.988382i | ||||
\(699\) | 11.3970 | 0.431076 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.9399 | 1.84843 | 0.924216 | − | 0.381869i | \(-0.124719\pi\) | ||||
0.924216 | + | 0.381869i | \(0.124719\pi\) | |||||||
\(702\) | 4.19374 | + | 1.36263i | 0.158283 | + | 0.0514291i | ||||
\(703\) | 9.08373 | − | 12.5027i | 0.342599 | − | 0.471548i | ||||
\(704\) | −28.4440 | − | 20.6658i | −1.07203 | − | 0.778872i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.7401 | + | 12.1624i | −0.630023 | + | 0.457739i | ||||
\(707\) | 26.6623i | 1.00274i | ||||||||
\(708\) | 14.7343 | + | 20.2801i | 0.553750 | + | 0.762172i | ||||
\(709\) | −7.65850 | − | 23.5705i | −0.287621 | − | 0.885207i | −0.985601 | − | 0.169089i | \(-0.945917\pi\) |
0.697980 | − | 0.716118i | \(-0.254083\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.949501 | − | 2.92226i | 0.0356091 | − | 0.109593i | ||||
\(712\) | −0.981187 | + | 0.318807i | −0.0367716 | + | 0.0119478i | ||||
\(713\) | −2.18302 | + | 0.709306i | −0.0817547 | + | 0.0265637i | ||||
\(714\) | 17.1637 | − | 52.8244i | 0.642334 | − | 1.97690i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.84112 | − | 17.9771i | −0.218293 | − | 0.671836i | ||||
\(717\) | 4.05614 | + | 5.58280i | 0.151479 | + | 0.208494i | ||||
\(718\) | − | 14.1746i | − | 0.528992i | ||||||
\(719\) | −14.7379 | + | 10.7077i | −0.549631 | + | 0.399331i | −0.827650 | − | 0.561245i | \(-0.810322\pi\) |
0.278018 | + | 0.960576i | \(0.410322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.41134 | + | 6.11119i | 0.313255 | + | 0.227593i | ||||
\(722\) | −14.2330 | + | 19.5900i | −0.529697 | + | 0.729065i | ||||
\(723\) | −27.0545 | − | 8.79052i | −1.00617 | − | 0.326923i | ||||
\(724\) | 1.15576 | 0.0429534 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.66224 | 0.210145 | ||||||||
\(727\) | 15.8540 | + | 5.15129i | 0.587994 | + | 0.191051i | 0.587878 | − | 0.808949i | \(-0.299963\pi\) |
0.000115145 | 1.00000i | \(0.499963\pi\) | ||||||||
\(728\) | 13.7752 | − | 18.9599i | 0.510542 | − | 0.702701i | ||||
\(729\) | 0.809017 | + | 0.587785i | 0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −59.9657 | + | 43.5676i | −2.21791 | + | 1.61141i | ||||
\(732\) | 22.6998i | 0.839008i | ||||||||
\(733\) | 11.7935 | + | 16.2324i | 0.435604 | + | 0.599558i | 0.969228 | − | 0.246164i | \(-0.0791702\pi\) |
−0.533624 | + | 0.845722i | \(0.679170\pi\) | |||||||
\(734\) | −20.8971 | − | 64.3147i | −0.771326 | − | 2.37390i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.66092 | − | 20.5002i | 0.245525 | − | 0.755648i | ||||
\(737\) | −27.9922 | + | 9.09522i | −1.03111 | + | 0.335027i | ||||
\(738\) | 3.75317 | − | 1.21948i | 0.138156 | − | 0.0448896i | ||||
\(739\) | 10.5242 | − | 32.3903i | 0.387140 | − | 1.19149i | −0.547776 | − | 0.836625i | \(-0.684525\pi\) |
0.934916 | − | 0.354870i | \(-0.115475\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.70964 | − | 5.26174i | −0.0628053 | − | 0.193295i | ||||
\(742\) | −17.8473 | − | 24.5647i | −0.655196 | − | 0.901800i | ||||
\(743\) | 38.5355i | 1.41373i | 0.707348 | + | 0.706865i | \(0.249891\pi\) | ||||
−0.707348 | + | 0.706865i | \(0.750109\pi\) | |||||||
\(744\) | −1.21370 | + | 0.881804i | −0.0444963 | + | 0.0323285i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −63.9026 | − | 46.4280i | −2.33964 | − | 1.69985i | ||||
\(747\) | 5.94559 | − | 8.18340i | 0.217538 | − | 0.299415i | ||||
\(748\) | −66.7055 | − | 21.6739i | −2.43900 | − | 0.792478i | ||||
\(749\) | 24.6244 | 0.899754 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0351 | −1.31494 | −0.657470 | − | 0.753481i | \(-0.728373\pi\) | ||||
−0.657470 | + | 0.753481i | \(0.728373\pi\) | |||||||
\(752\) | −9.85187 | − | 3.20107i | −0.359261 | − | 0.116731i | ||||
\(753\) | −7.24494 | + | 9.97181i | −0.264020 | + | 0.363393i | ||||
\(754\) | −9.11807 | − | 6.62466i | −0.332060 | − | 0.241256i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 9.93354 | − | 7.21714i | 0.361279 | − | 0.262485i | ||||
\(757\) | 35.0131i | 1.27257i | 0.771453 | + | 0.636287i | \(0.219530\pi\) | ||||
−0.771453 | + | 0.636287i | \(0.780470\pi\) | |||||||
\(758\) | 6.40322 | + | 8.81328i | 0.232576 | + | 0.320113i | ||||
\(759\) | −4.97281 | − | 15.3047i | −0.180502 | − | 0.555527i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.69007 | − | 29.8230i | 0.351265 | − | 1.08108i | −0.606879 | − | 0.794794i | \(-0.707579\pi\) |
0.958144 | − | 0.286288i | \(-0.0924213\pi\) | |||||||
\(762\) | 23.6389 | − | 7.68074i | 0.856347 | − | 0.278244i | ||||
\(763\) | −44.0497 | + | 14.3126i | −1.59471 | + | 0.518152i | ||||
\(764\) | 3.78123 | − | 11.6374i | 0.136800 | − | 0.421027i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.37534 | − | 28.8543i | −0.338745 | − | 1.04255i | ||||
\(767\) | −7.83742 | − | 10.7873i | −0.282993 | − | 0.389506i | ||||
\(768\) | − | 23.8400i | − | 0.860253i | ||||||
\(769\) | 1.94014 | − | 1.40959i | 0.0699633 | − | 0.0508313i | −0.552254 | − | 0.833676i | \(-0.686232\pi\) |
0.622217 | + | 0.782845i | \(0.286232\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.8497 | + | 12.2421i | 0.606829 | + | 0.440887i | ||||
\(772\) | −50.3960 | + | 69.3641i | −1.81379 | + | 2.49647i | ||||
\(773\) | 10.3880 | + | 3.37526i | 0.373630 | + | 0.121400i | 0.489812 | − | 0.871828i | \(-0.337065\pi\) |
−0.116182 | + | 0.993228i | \(0.537065\pi\) | |||||||
\(774\) | −25.6788 | −0.923004 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −37.3508 | −1.34082 | ||||||||
\(777\) | −17.3507 | − | 5.63760i | −0.622454 | − | 0.202248i | ||||
\(778\) | 24.2152 | − | 33.3293i | 0.868156 | − | 1.19491i | ||||
\(779\) | −4.00568 | − | 2.91030i | −0.143519 | − | 0.104272i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.72774 | + | 1.25528i | −0.0618236 | + | 0.0449174i | ||||
\(782\) | − | 87.5792i | − | 3.13183i | ||||||
\(783\) | −1.50234 | − | 2.06779i | −0.0536893 | − | 0.0738970i | ||||
\(784\) | −2.18917 | − | 6.73757i | −0.0781846 | − | 0.240627i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.55696 | − | 20.1802i | 0.233879 | − | 0.719806i | ||||
\(787\) | −11.0060 | + | 3.57607i | −0.392321 | + | 0.127473i | −0.498533 | − | 0.866871i | \(-0.666128\pi\) |
0.106212 | + | 0.994344i | \(0.466128\pi\) | |||||||
\(788\) | 50.1599 | − | 16.2979i | 1.78687 | − | 0.580590i | ||||
\(789\) | 0.690704 | − | 2.12577i | 0.0245897 | − | 0.0756794i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.7847 | + | 33.1918i | 0.383459 | + | 1.18017i | ||||
\(792\) | −6.18216 | − | 8.50901i | −0.219673 | − | 0.302354i | ||||
\(793\) | − | 12.0744i | − | 0.428773i | ||||||
\(794\) | −51.3837 | + | 37.3324i | −1.82354 | + | 1.32488i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32.3096 | + | 23.4743i | 1.14518 | + | 0.832026i | ||||
\(797\) | 12.8680 | − | 17.7113i | 0.455808 | − | 0.627366i | −0.517825 | − | 0.855487i | \(-0.673258\pi\) |
0.973633 | + | 0.228121i | \(0.0732581\pi\) | |||||||
\(798\) | −22.9610 | − | 7.46048i | −0.812810 | − | 0.264098i | ||||
\(799\) | 50.8367 | 1.79847 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.287512 | 0.0101587 | ||||||||
\(802\) | −35.7259 | − | 11.6081i | −1.26153 | − | 0.409895i | ||||
\(803\) | 6.18970 | − | 8.51940i | 0.218430 | − | 0.300643i | ||||
\(804\) | −28.6476 | − | 20.8137i | −1.01032 | − | 0.734043i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.49148 | − | 1.08362i | 0.0525350 | − | 0.0381689i | ||||
\(807\) | 19.3036i | 0.679520i | ||||||||
\(808\) | 16.1507 | + | 22.2295i | 0.568180 | + | 0.782033i | ||||
\(809\) | 6.65926 | + | 20.4951i | 0.234127 | + | 0.720570i | 0.997236 | + | 0.0742994i | \(0.0236721\pi\) |
−0.763109 | + | 0.646270i | \(0.776328\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.5848 | + | 41.8098i | −0.477028 | + | 1.46814i | 0.366175 | + | 0.930546i | \(0.380667\pi\) |
−0.843203 | + | 0.537596i | \(0.819333\pi\) | |||||||
\(812\) | −29.8471 | + | 9.69791i | −1.04743 | + | 0.340330i | ||||
\(813\) | 11.3567 | − | 3.69001i | 0.398297 | − | 0.129414i | ||||
\(814\) | −11.1566 | + | 34.3365i | −0.391039 | + | 1.20349i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.89936 | − | 8.92331i | −0.101498 | − | 0.312378i | ||||
\(817\) | 18.9374 | + | 26.0651i | 0.662535 | + | 0.911901i | ||||
\(818\) | 72.8667i | 2.54772i | ||||||||
\(819\) | −5.28380 | + | 3.83891i | −0.184631 | + | 0.134142i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.1070 | − | 19.6944i | −0.946042 | − | 0.687340i | 0.00382568 | − | 0.999993i | \(-0.498782\pi\) |
−0.949867 | + | 0.312653i | \(0.898782\pi\) | |||||||
\(822\) | 27.1722 | − | 37.3993i | 0.947739 | − | 1.30445i | ||||
\(823\) | −53.2458 | − | 17.3006i | −1.85603 | − | 0.603061i | −0.995623 | − | 0.0934576i | \(-0.970208\pi\) |
−0.860409 | − | 0.509604i | \(-0.829792\pi\) | |||||||
\(824\) | 10.7148 | 0.373266 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −58.1857 | −2.02454 | ||||||||
\(827\) | −38.8126 | − | 12.6110i | −1.34965 | − | 0.438527i | −0.457074 | − | 0.889429i | \(-0.651103\pi\) |
−0.892574 | + | 0.450901i | \(0.851103\pi\) | |||||||
\(828\) | 11.3799 | − | 15.6631i | 0.395478 | − | 0.544329i | ||||
\(829\) | 0.0994391 | + | 0.0722468i | 0.00345366 | + | 0.00250923i | 0.589511 | − | 0.807761i | \(-0.299321\pi\) |
−0.586057 | + | 0.810270i | \(0.699321\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.1531 | − | 15.3686i | 0.733791 | − | 0.533131i | ||||
\(832\) | 22.4997i | 0.780036i | ||||||||
\(833\) | 20.4353 | + | 28.1267i | 0.708040 | + | 0.974534i | ||||
\(834\) | −8.46455 | − | 26.0512i | −0.293103 | − | 0.902080i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9.42094 | + | 28.9947i | −0.325830 | + | 1.00280i | ||||
\(837\) | 0.397622 | − | 0.129195i | 0.0137438 | − | 0.00446564i | ||||
\(838\) | 57.9408 | − | 18.8261i | 2.00153 | − | 0.650337i | ||||
\(839\) | −4.57603 | + | 14.0836i | −0.157982 | + | 0.486219i | −0.998451 | − | 0.0556411i | \(-0.982280\pi\) |
0.840469 | + | 0.541860i | \(0.182280\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.94275 | − | 21.3676i | −0.239405 | − | 0.736813i | ||||
\(842\) | −5.42552 | − | 7.46759i | −0.186976 | − | 0.257350i | ||||
\(843\) | 10.1219i | 0.348616i | ||||||||
\(844\) | 21.5191 | − | 15.6345i | 0.740717 | − | 0.538162i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14.2483 | + | 10.3520i | 0.489867 | + | 0.355910i | ||||
\(847\) | −4.92947 | + | 6.78483i | −0.169379 | + | 0.233130i | ||||
\(848\) | −4.87812 | − | 1.58500i | −0.167515 | − | 0.0544290i | ||||
\(849\) | −31.8638 | −1.09356 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.7664 | −0.986098 | ||||||||
\(852\) | −2.44359 | − | 0.793970i | −0.0837160 | − | 0.0272010i | ||||
\(853\) | −4.27011 | + | 5.87730i | −0.146206 | + | 0.201235i | −0.875839 | − | 0.482604i | \(-0.839691\pi\) |
0.729633 | + | 0.683839i | \(0.239691\pi\) | |||||||
\(854\) | −42.6269 | − | 30.9702i | −1.45866 | − | 1.05978i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.5304 | − | 14.9162i | 0.701715 | − | 0.509826i | ||||
\(857\) | − | 26.8175i | − | 0.916068i | −0.888935 | − | 0.458034i | \(-0.848554\pi\) | ||
0.888935 | − | 0.458034i | \(-0.151446\pi\) | |||||||
\(858\) | 7.59706 | + | 10.4565i | 0.259359 | + | 0.356978i | ||||
\(859\) | 6.36691 | + | 19.5953i | 0.217236 | + | 0.668584i | 0.998987 | + | 0.0449937i | \(0.0143268\pi\) |
−0.781751 | + | 0.623591i | \(0.785673\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.80621 | + | 5.55893i | −0.0615554 | + | 0.189448i | ||||
\(862\) | 79.2876 | − | 25.7621i | 2.70055 | − | 0.877461i | ||||
\(863\) | 13.0759 | − | 4.24862i | 0.445109 | − | 0.144625i | −0.0778827 | − | 0.996963i | \(-0.524816\pi\) |
0.522991 | + | 0.852338i | \(0.324816\pi\) | |||||||
\(864\) | −1.21324 | + | 3.73397i | −0.0412753 | + | 0.127032i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.33413 | + | 22.5721i | 0.249224 | + | 0.767033i | ||||
\(867\) | 17.0723 | + | 23.4981i | 0.579807 | + | 0.798036i | ||||
\(868\) | − | 5.13346i | − | 0.174241i | ||||||
\(869\) | 7.28622 | − | 5.29375i | 0.247168 | − | 0.179578i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.2381 | + | 11.0711i | 0.516324 | + | 0.375131i | ||||
\(872\) | −28.0563 | + | 38.6162i | −0.950107 | + | 1.30771i | ||||
\(873\) | 9.89959 | + | 3.21657i | 0.335050 | + | 0.108864i | ||||
\(874\) | −38.0678 | −1.28766 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.6693 | 0.428055 | ||||||||
\(877\) | 20.9641 | + | 6.81166i | 0.707909 | + | 0.230014i | 0.640773 | − | 0.767730i | \(-0.278614\pi\) |
0.0671357 | + | 0.997744i | \(0.478614\pi\) | |||||||
\(878\) | −9.81840 | + | 13.5139i | −0.331355 | + | 0.456071i | ||||
\(879\) | −13.4487 | − | 9.77103i | −0.453612 | − | 0.329569i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.31294 | − | 5.31316i | 0.246379 | − | 0.179005i | −0.457741 | − | 0.889085i | \(-0.651341\pi\) |
0.704121 | + | 0.710080i | \(0.251341\pi\) | |||||||
\(882\) | 12.0446i | 0.405561i | ||||||||
\(883\) | −0.941165 | − | 1.29540i | −0.0316727 | − | 0.0435937i | 0.792887 | − | 0.609369i | \(-0.208577\pi\) |
−0.824560 | + | 0.565775i | \(0.808577\pi\) | |||||||
\(884\) | 13.8701 | + | 42.6879i | 0.466503 | + | 1.43575i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.0259 | − | 46.2450i | 0.504805 | − | 1.55363i | ||||
\(887\) | −16.5724 | + | 5.38470i | −0.556447 | + | 0.180801i | −0.573722 | − | 0.819050i | \(-0.694501\pi\) |
0.0172750 | + | 0.999851i | \(0.494501\pi\) | |||||||
\(888\) | −17.8811 | + | 5.80991i | −0.600049 | + | 0.194968i | ||||
\(889\) | −11.3762 | + | 35.0123i | −0.381545 | + | 1.17427i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.905762 | + | 2.78765i | 0.0303442 | + | 0.0933897i | ||||
\(892\) | 16.1580 | + | 22.2396i | 0.541011 | + | 0.744638i | ||||
\(893\) | − | 22.0970i | − | 0.739448i | ||||||
\(894\) | 13.9410 | − | 10.1287i | 0.466257 | − | 0.338756i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 57.3129 | + | 41.6403i | 1.91469 | + | 1.39110i | ||||
\(897\) | −6.05314 | + | 8.33143i | −0.202108 | + | 0.278178i | ||||
\(898\) | −43.5842 | − | 14.1614i | −1.45442 | − | 0.472571i | ||||
\(899\) | −1.06860 | −0.0356397 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.1716 | 0.838588 | ||||||||
\(902\) | 11.0009 | + | 3.57442i | 0.366291 | + | 0.119015i | ||||
\(903\) | 22.3556 | − | 30.7698i | 0.743947 | − | 1.02396i | ||||
\(904\) | 29.0976 | + | 21.1406i | 0.967772 | + | 0.703128i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −31.8291 | + | 23.1252i | −1.05745 | + | 0.768283i | ||||
\(907\) | − | 20.8690i | − | 0.692942i | −0.938061 | − | 0.346471i | \(-0.887380\pi\) | ||
0.938061 | − | 0.346471i | \(-0.112620\pi\) | |||||||
\(908\) | −26.5976 | − | 36.6085i | −0.882673 | − | 1.21489i | ||||
\(909\) | −2.36628 | − | 7.28266i | −0.0784845 | − | 0.241550i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.1958 | − | 46.7680i | 0.503461 | − | 1.54949i | −0.299882 | − | 0.953976i | \(-0.596947\pi\) |
0.803343 | − | 0.595517i | \(-0.203053\pi\) | |||||||
\(912\) | −3.87866 | + | 1.26025i | −0.128435 | + | 0.0417312i | ||||
\(913\) | 28.1977 | − | 9.16200i | 0.933209 | − | 0.303218i | ||||
\(914\) | 3.15418 | − | 9.70758i | 0.104331 | − | 0.321098i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.8045 | − | 48.6413i | −0.522196 | − | 1.60715i | ||||
\(917\) | 18.4728 | + | 25.4256i | 0.610025 | + | 0.839627i | ||||
\(918\) | 15.9519i | 0.526492i | ||||||||
\(919\) | −9.05765 | + | 6.58077i | −0.298784 | + | 0.217079i | −0.727069 | − | 0.686564i | \(-0.759118\pi\) |
0.428285 | + | 0.903644i | \(0.359118\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.4592 | − | 8.32559i | −0.377593 | − | 0.274338i | ||||
\(922\) | 16.2908 | − | 22.4224i | 0.536510 | − | 0.738443i | ||||
\(923\) | 1.29978 | + | 0.422325i | 0.0427829 | + | 0.0139010i | ||||
\(924\) | 35.9897 | 1.18397 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21.3425 | −0.701357 | ||||||||
\(927\) | −2.83987 | − | 0.922731i | −0.0932737 | − | 0.0303065i | ||||
\(928\) | 5.89838 | − | 8.11842i | 0.193624 | − | 0.266500i | ||||
\(929\) | 39.0181 | + | 28.3483i | 1.28014 | + | 0.930077i | 0.999557 | − | 0.0297529i | \(-0.00947204\pi\) |
0.280584 | + | 0.959830i | \(0.409472\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.2258 | − | 8.88253i | 0.400683 | − | 0.291113i | ||||
\(932\) | 40.1906i | 1.31649i | ||||||||
\(933\) | −8.84615 | − | 12.1757i | −0.289610 | − | 0.398614i | ||||
\(934\) | 25.3662 | + | 78.0690i | 0.830006 | + | 2.55450i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.07992 | + | 6.40133i | −0.0679842 | + | 0.209234i | ||||
\(937\) | −48.0661 | + | 15.6176i | −1.57025 | + | 0.510205i | −0.959522 | − | 0.281635i | \(-0.909123\pi\) |
−0.610728 | + | 0.791840i | \(0.709123\pi\) | |||||||
\(938\) | 78.1702 | − | 25.3990i | 2.55235 | − | 0.829308i | ||||
\(939\) | −1.10466 | + | 3.39980i | −0.0360493 | + | 0.110948i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.7934 | − | 36.2965i | −0.384455 | − | 1.18323i | −0.936875 | − | 0.349665i | \(-0.886295\pi\) |
0.552420 | − | 0.833566i | \(-0.313705\pi\) | |||||||
\(942\) | 10.8972 | + | 14.9987i | 0.355051 | + | 0.488686i | ||||
\(943\) | 9.21634i | 0.300125i | ||||||||
\(944\) | −7.95180 | + | 5.77732i | −0.258809 | + | 0.188036i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −60.8924 | − | 44.2409i | −1.97978 | − | 1.43840i | ||||
\(947\) | 14.4119 | − | 19.8363i | 0.468323 | − | 0.644592i | −0.507885 | − | 0.861425i | \(-0.669573\pi\) |
0.976209 | + | 0.216833i | \(0.0695726\pi\) | |||||||
\(948\) | 10.3051 | + | 3.34832i | 0.334693 | + | 0.108748i | ||||
\(949\) | −6.73897 | −0.218756 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.7820 | −0.414484 | ||||||||
\(952\) | 80.6311 | + | 26.1986i | 2.61327 | + | 0.849103i | ||||
\(953\) | −7.64232 | + | 10.5187i | −0.247559 | + | 0.340736i | −0.914655 | − | 0.404236i | \(-0.867537\pi\) |
0.667096 | + | 0.744972i | \(0.267537\pi\) | |||||||
\(954\) | 7.05501 | + | 5.12576i | 0.228414 | + | 0.165953i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −19.6872 | + | 14.3036i | −0.636729 | + | 0.462611i | ||||
\(957\) | − | 7.49172i | − | 0.242173i | ||||||
\(958\) | −11.9476 | − | 16.4444i | −0.386008 | − | 0.531295i | ||||
\(959\) | 21.1583 | + | 65.1187i | 0.683239 | + | 2.10279i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.52551 | + | 29.3165i | −0.307275 | + | 0.945694i | ||||
\(962\) | 21.9735 | − | 7.13962i | 0.708453 | − | 0.230190i | ||||
\(963\) | −6.72600 | + | 2.18541i | −0.216742 | + | 0.0704238i | ||||
\(964\) | 30.9989 | − | 95.4048i | 0.998408 | − | 3.07278i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 13.8869 | + | 42.7395i | 0.446804 | + | 1.37512i | ||||
\(967\) | 25.4636 | + | 35.0476i | 0.818854 | + | 1.12706i | 0.989896 | + | 0.141792i | \(0.0452864\pi\) |
−0.171043 | + | 0.985264i | \(0.554714\pi\) | |||||||
\(968\) | 8.64284i | 0.277791i | ||||||||
\(969\) | 16.1919 | − | 11.7641i | 0.520159 | − | 0.377918i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.8922 | + | 17.3587i | 0.766738 | + | 0.557068i | 0.900970 | − | 0.433882i | \(-0.142857\pi\) |
−0.134231 | + | 0.990950i | \(0.542857\pi\) | |||||||
\(972\) | −2.07277 | + | 2.85292i | −0.0664840 | + | 0.0915074i | ||||
\(973\) | 38.5853 | + | 12.5371i | 1.23699 | + | 0.401921i | ||||
\(974\) | −6.68721 | −0.214272 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.90056 | −0.284900 | ||||||||
\(977\) | −57.6486 | − | 18.7312i | −1.84434 | − | 0.599263i | −0.997752 | − | 0.0670189i | \(-0.978651\pi\) |
−0.846591 | − | 0.532244i | \(-0.821349\pi\) | |||||||
\(978\) | −13.7348 | + | 18.9044i | −0.439191 | + | 0.604495i | ||||
\(979\) | 0.681782 | + | 0.495343i | 0.0217898 | + | 0.0158312i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.7617 | − | 7.81882i | 0.343594 | − | 0.249636i | ||||
\(982\) | 86.5202i | 2.76097i | ||||||||
\(983\) | −23.6757 | − | 32.5868i | −0.755138 | − | 1.03936i | −0.997603 | − | 0.0691986i | \(-0.977956\pi\) |
0.242465 | − | 0.970160i | \(-0.422044\pi\) | |||||||
\(984\) | 1.86141 | + | 5.72884i | 0.0593397 | + | 0.182629i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 12.5993 | − | 38.7766i | 0.401243 | − | 1.23490i | ||||
\(987\) | −24.8088 | + | 8.06087i | −0.789673 | + | 0.256580i | ||||
\(988\) | 18.5550 | − | 6.02888i | 0.590313 | − | 0.191804i | ||||
\(989\) | 18.5320 | − | 57.0357i | 0.589284 | − | 1.81363i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.7889 | + | 36.2824i | 0.374485 | + | 1.15255i | 0.943825 | + | 0.330445i | \(0.107199\pi\) |
−0.569340 | + | 0.822102i | \(0.692801\pi\) | |||||||
\(992\) | 0.964821 | + | 1.32796i | 0.0306331 | + | 0.0421628i | ||||
\(993\) | 4.70504i | 0.149310i | ||||||||
\(994\) | 4.82485 | − | 3.50546i | 0.153035 | − | 0.111186i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 28.8580 | + | 20.9665i | 0.914399 | + | 0.664350i | ||||
\(997\) | 15.6220 | − | 21.5018i | 0.494753 | − | 0.680969i | −0.486503 | − | 0.873679i | \(-0.661728\pi\) |
0.981256 | + | 0.192710i | \(0.0617277\pi\) | |||||||
\(998\) | −13.0966 | − | 4.25534i | −0.414565 | − | 0.134700i | ||||
\(999\) | 5.23959 | 0.165773 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 375.2.i.c.274.4 | 16 | ||
5.2 | odd | 4 | 375.2.g.e.226.1 | 16 | |||
5.3 | odd | 4 | 375.2.g.d.226.4 | 16 | |||
5.4 | even | 2 | 75.2.i.a.4.1 | ✓ | 16 | ||
15.14 | odd | 2 | 225.2.m.b.154.4 | 16 | |||
25.6 | even | 5 | 75.2.i.a.19.1 | yes | 16 | ||
25.8 | odd | 20 | 375.2.g.d.151.4 | 16 | |||
25.9 | even | 10 | 1875.2.b.h.1249.2 | 16 | |||
25.12 | odd | 20 | 1875.2.a.m.1.2 | 8 | |||
25.13 | odd | 20 | 1875.2.a.p.1.7 | 8 | |||
25.16 | even | 5 | 1875.2.b.h.1249.15 | 16 | |||
25.17 | odd | 20 | 375.2.g.e.151.1 | 16 | |||
25.19 | even | 10 | inner | 375.2.i.c.349.4 | 16 | ||
75.38 | even | 20 | 5625.2.a.t.1.2 | 8 | |||
75.56 | odd | 10 | 225.2.m.b.19.4 | 16 | |||
75.62 | even | 20 | 5625.2.a.bd.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.4.1 | ✓ | 16 | 5.4 | even | 2 | ||
75.2.i.a.19.1 | yes | 16 | 25.6 | even | 5 | ||
225.2.m.b.19.4 | 16 | 75.56 | odd | 10 | |||
225.2.m.b.154.4 | 16 | 15.14 | odd | 2 | |||
375.2.g.d.151.4 | 16 | 25.8 | odd | 20 | |||
375.2.g.d.226.4 | 16 | 5.3 | odd | 4 | |||
375.2.g.e.151.1 | 16 | 25.17 | odd | 20 | |||
375.2.g.e.226.1 | 16 | 5.2 | odd | 4 | |||
375.2.i.c.274.4 | 16 | 1.1 | even | 1 | trivial | ||
375.2.i.c.349.4 | 16 | 25.19 | even | 10 | inner | ||
1875.2.a.m.1.2 | 8 | 25.12 | odd | 20 | |||
1875.2.a.p.1.7 | 8 | 25.13 | odd | 20 | |||
1875.2.b.h.1249.2 | 16 | 25.9 | even | 10 | |||
1875.2.b.h.1249.15 | 16 | 25.16 | even | 5 | |||
5625.2.a.t.1.2 | 8 | 75.38 | even | 20 | |||
5625.2.a.bd.1.7 | 8 | 75.62 | even | 20 |